The Unique Minimum State Variable RE Solution is E-Stable in All Well Formulated Linear Models
This paper explores the relationship between the closely linked concepts of E-stability and least-squares learnability, featured in recent work by Evans and Honkapohja (1999, 2001), and the minimum-state-variable (MSV) solution defined by McCallum (1983) and used by many researchers for rational expectations (RE) analysis. It is shown that the MSV solution, which is unique by construction, is E-stable--and therefore LS learnable when nonexplosive--in all linear RE models that satisfy conditions for being well formulated.' The latter property involves two requirements. The first is that values of the model's parameters are restricted so as to avoid any infinite discontinuity, of the steady state values of endogenous variables, in response to small changes in these parameters. (It is expressed in terms of the eigenvalues of a matrix that is the sum of those attached to the one-period-ahead and one-period-lagged values of the endogenous variables in a first-order vector formulation of the model.) The second, which is needed infrequently, is that the parameters are restricted to prevent any infinite discontinuities in the MSV response coefficients.
|Date of creation:||Sep 2003|
|Date of revision:|
|Publication status:||published as McCallum, Bennett T. "On The Relationship Between Determinate And CSV Solutions In Linear Re Models," Economics Letters, 2004, v84(1,Jul), 55-60.|
|Contact details of provider:|| Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.|
Web page: http://www.nber.org
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Wenzelburger, Jan, 2006. "Learning in linear models with expectational leads," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 854-884, November.
- John H. Cochrane, 1998.
"A Frictionless View of U.S. Inflation,"
CRSP working papers
479, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
- Flood, Robert P & Garber, Peter M, 1980. "An Economic Theory of Monetary Reform," Journal of Political Economy, University of Chicago Press, vol. 88(1), pages 24-58, February.
- Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 1998.
"The perils of Taylor Rules,"
Departmental Working Papers
199831, Rutgers University, Department of Economics.
- Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 1998. "The Perils of Taylor Rules," Working Papers 98-37, C.V. Starr Center for Applied Economics, New York University.
- Benhabib, Jess & Schmitt-Grohé, Stephanie & Uribe, Martín, 1999. "The Perils of Taylor Rules," CEPR Discussion Papers 2314, C.E.P.R. Discussion Papers.
- McCallum, Bennett T., 1983.
"On non-uniqueness in rational expectations models : An attempt at perspective,"
Journal of Monetary Economics,
Elsevier, vol. 11(2), pages 139-168.
- Bennett T. McCallum, 1981. "On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective," NBER Working Papers 0684, National Bureau of Economic Research, Inc.
- Robert G. King, 2000. "The new IS-LM model : language, logic, and limits," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 45-103.
- Binder,M. & Pesaran,H.M., 1995.
"Multivariate Rational Expectations Models and Macroeconomic Modelling: A Review and Some New Results,"
Cambridge Working Papers in Economics
9415, Faculty of Economics, University of Cambridge.
- Michael Binder & M. Hashem Pesaran, 1994. "GAUSS and Matlab codes for Multivariate Rational Expectations Models and Macroeconometric Modelling: A Review and Some New Results," QM&RBC Codes 74, Quantitative Macroeconomics & Real Business Cycles.
- Narayana R. Kocherlakota & Christopher Phelan, 1999. "Explaining the fiscal theory of the price level," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 14-23.
- Desgranges, G. & Gauthier, S., 1999. "On the Uniqueness of the Bubble-Free Solution in Linear Rational Expectations Models," G.R.E.Q.A.M. 99a45, Universite Aix-Marseille III.
- Bullard, James & Mitra, Kaushik, 2002.
"Learning about monetary policy rules,"
Journal of Monetary Economics,
Elsevier, vol. 49(6), pages 1105-1129, September.
- repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
- King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
- Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
- Gauthier, St phane, 2003.
"Dynamic Equivalence Principle In Linear Rational Expectations Models,"
Cambridge University Press, vol. 7(01), pages 63-88, February.
- Stéphane Gauthier, 2003. "Dynamic equivalence principle in linear rational expectations models," Post-Print halshs-00069499, HAL.
- Sims, Christopher A, 1994. "A Simple Model for Study of the Determination of the Price Level and the Interaction of Monetary and Fiscal Policy," Economic Theory, Springer, vol. 4(3), pages 381-99.
- G. Desgranges & Stéphane Gauthier, 2003.
"Uniqueness of bubble-free solution in linear rational expectations models,"
- Desgranges, Gabriel & Gauthier, St phane, 2003. "Uniqueness Of Bubble-Free Solution In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(02), pages 171-191, April.
- Ben S. Bernanke & Michael Woodford, 1997.
"Inflation forecasts and monetary policy,"
Federal Reserve Bank of Cleveland, pages 653-686.
- Stephen J. DeCanio, 1979. "Rational Expectations and Learning from Experience," The Quarterly Journal of Economics, Oxford University Press, vol. 93(1), pages 47-57.
- Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
- Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
- repec:cup:macdyn:v:7:y:2003:i:1:p:63-88 is not listed on IDEAS
- George Evans, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, Oxford University Press, vol. 100(4), pages 1217-1233.
- Robert A. Driskill, 2002. "A Proposal for a Selection Criterion in a Class of Dynamic Rational Expectations Models with Multiple Equilibria," Vanderbilt University Department of Economics Working Papers 0210, Vanderbilt University Department of Economics.
- Evans, George W & Honkapohja, Seppo, 1992. "On the Robustness of Bubbles in Linear RE Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 1-14, February.
- Bennett T. McCallum, 2002. "Consistent Expectations, Rational Expectations, Multiple-Solution Indeterminacies, and Least-Squares Learnability," NBER Working Papers 9218, National Bureau of Economic Research, Inc.
- Michael Woodford, 1994. "Nonstandard Indicators for Monetary Policy: Can Their Usefulness Be Judged from Forecasting Regressions?," NBER Chapters, in: Monetary Policy, pages 95-115 National Bureau of Economic Research, Inc.
When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:9960. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.